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Incoming links: Horizontal chemical quenching
Past exam of the mathematics course of the University of Cambridge 2018 iii Paper 315 3 a Solution Created 2026-10-03 Updated 2026-10-05
Four mechanisms that can produce disequilibrium chemistry in an exoplanet atmosphere are:
- Atmospheric photochemistry. Stellar ultraviolet photons initiate reactions whose products need not follow local thermochemical equilibrium. The ozone layer on Earth is a solar-system example. Calculations for HD 189733 b predict enhanced hydrogen cyanide and acetylene from the processing of methane and ammonia; these are model examples rather than assertions of an unambiguous detection.
- Vertical transport and chemical quenching. When the eddy mixing time is shorter than the chemical relaxation time, gas retains a deeper abundance above its chemical quench level. The excess carbon monoxide in Jupiter's cool atmosphere exemplifies carbon monoxide–methane quenching. Models of HD 189733 b predict quenched methane and ammonia abundances differing from their local chemical equilibrium values. The enhancement or depletion depends on the underlying atmospheric pressure-temperature profile.
- Horizontal chemical quenching. If the atmospheric advection time is short, winds move chemically processed gas into regions with different irradiation or temperature faster than it can re-equilibrate. Transport of gas within Earth's ozone layer moves material away from its local photochemical production regions. Models of HD 209458 b show that dayside carbon monoxide-rich composition can persist into the cooler nightside instead of forming the local chemical equilibrium amount of methane.
- Condensation with sedimentation or rainout. Finite-rate cloud formation can depart from phase equilibrium, while atmospheric condensate rainout removes elements from a layer and changes its gas composition. Earth's water atmospheric cold trap limits the supply of water to the stratosphere. In HD 209458 b models, titanium-bearing condensates can settle and suppress upper-atmospheric titanium monoxide. The remaining gas can still be in local chemical equilibrium with its depleted inventory: rainout is an open-column effect, not necessarily a failure of equilibrium among all gas reactions.
The exoplanet transport and photochemical examples follow kinetic atmosphere calculations and models including horizontal transport; the condensate example is examined in cold-trap calculations.
Past exam of the mathematics course of the University of Cambridge 2018 iii Paper 315 3 b i Solution Created 2026-10-03 Updated 2026-10-05
Take the logarithm to base ten and write pressure in units of , so its argument is dimensionless. Continuity of the atmospheric pressure-temperature profile givesThusIf the logarithm means , the equivalent constant is . A plot of temperature against logarithmic pressure is vertical in each isothermal region and straight between the two endpoints.
The processes can be organized by the supplied pressure ranges, although the exact boundaries require reaction rates, irradiation and mixing information:
- At , the dense gas can approach thermochemical equilibrium because collisions and reactions are relatively rapid. Deep carbon monoxide and molecular nitrogen can provide reservoirs for transported material.
- At , the falling temperature slows chemical conversion. Vertical transport can produce a chemical quench level when the chemical relaxation time crosses the eddy mixing time. Horizontal chemical quenching is also possible if dayside and nightside conditions differ. Suitable species can condense and undergo atmospheric condensate rainout where a saturation curve is crossed.
- At , slow thermal chemistry permits a quenched atmospheric mixing ratio to survive. Atmospheric photochemistry can dominate where stellar ultraviolet photons penetrate, often at still lower pressures; atmospheric haze may form from its products. Extremely high layers can also experience atmospheric escape.
The profile identifies plausible chemical regimes, but does not fix their transition pressures by itself. In particular, cloud formation depends on the species-specific condensation curve, and ultraviolet processing depends on shielding.